Hostname: page-component-77c89778f8-gq7q9 Total loading time: 0 Render date: 2024-07-19T16:15:55.510Z Has data issue: false hasContentIssue false

Experimental study of submerged liquid metal jet in a rectangular duct in a transverse magnetic field

Published online by Cambridge University Press:  06 December 2022

Ivan A. Belyaev*
Joint Institute for High Temperature RAS, Izhorskaya 13 Bd. 2, 125412 Moscow, Russia Moscow Power Engineering Institute, Krasnokazarmennaya 14, 111250 Moscow, Russia
Ivan S. Mironov
Joint Institute for High Temperature RAS, Izhorskaya 13 Bd. 2, 125412 Moscow, Russia
Nikita A. Luchinkin
Moscow Power Engineering Institute, Krasnokazarmennaya 14, 111250 Moscow, Russia
Yaroslav I. Listratov
Moscow Power Engineering Institute, Krasnokazarmennaya 14, 111250 Moscow, Russia
Yuri B. Kolesnikov
Technische Universitat Ilmenau, PF 100565, 98684 Ilmenau, Germany
Dmitry Kransov
Technische Universitat Ilmenau, PF 100565, 98684 Ilmenau, Germany
Oleg Zikanov
University of Michigan-Dearborn, Dearborn, MI 48128-1491, USA
Sergei Molokov
Technische Universitat Ilmenau, PF 100565, 98684 Ilmenau, Germany
Email address for correspondence:


A liquid metal flow in the form of a submerged round jet entering a square duct in the presence of a transverse magnetic field is studied experimentally. A range of high Reynolds and Hartmann numbers is considered. Flow velocity is measured using electric potential difference probes. A detailed study of the flow in the duct's cross-section about seven jet's diameters downstream of the inlet reveals the dynamics, which is unsteady and dominated by high-amplitude fluctuations resulting from the instability of the jet. The flow structure and fluctuation properties are largely determined by the value of the Stuart number ${{N}}$. At moderate ${{N}}$, the mean velocity profile retains a central jet with three-dimensional perturbations increasingly suppressed by the magnetic field as ${{N}}$ grows. At higher values of ${{N}}$, the flow becomes quasi-two-dimensional and acquires the form of an asymmetric macrovortex, with high-amplitude velocity fluctuations reemerging.

JFM Papers
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)



Abdou, M., Morley, N.B., Smolentsev, S., Ying, A., Malang, S., Rowcliffe, A. & Ulrickson, M. 2015 Blanket/first wall challenges and required R&D on the pathway to DEMO. Fusion Engng Des. 100, 243.Google Scholar
Alemany, A., Moreau, R., Sulem, P.L. & Frisch, U. 1979 Influence of an external magnetic field on homogeneous MHD turbulence. J. Fluid Mech. 18, 277313.Google Scholar
Anghan, C., Dave, S., Saincher, S. & Banerjee, J. 2019 Direct numerical simulation of transitional and turbulent round jets: evolution of vortical structures and turbulence budget. Phys. Fluids 31 (6), 065105.Google Scholar
Belyaev, I., Krasnov, D., Kolesnikov, Y., Biryukov, D., Chernysh, D., Zikanov, O. & Listratov, Y. 2020 Effects of symmetry on magnetohydrodynamic mixed convection flow in a vertical duct. Phys. Fluids 32, 094106.Google Scholar
Belyaev, I.A., Pyatnitskaya, N.Yu., Luchinkin, N.A., Krasnov, D, Kolesnikov, Yu.B., Listratov, Ya.I., Mironov, I.S., Zikanov, O. & Sviridov, E.V. 2021 Flat liquid metal jet affected by a transverse magnetic field. Magnetohydrodynamics 57 (2), 211222.Google Scholar
Belyaev, I.A., Sviridov, V.G., Batenin, V.M., Biryukov, D.A., Nikitina, I.S., Manchkha, S.P., Pyatnitskaya, N.Yu., Razuvanov, N.G. & Sviridov, E.V. 2017 Test facility for investigation of heat transfer of promising coolants for the nuclear power industry. Therm. Engng 64 (11), 841848.Google Scholar
Bobkov, V., Fokin, L., Petrov, E., Popov, V., Rumiantsev, V. & Savvatimsky, A. 2008 Thermophysical properties of materials for nuclear engineering: a tutorial and collection of data. IAEA, Vienna.Google Scholar
Branover, H. 1978 Magnetohydrodynamic Flow in Ducts. Halstead Press & Israel Universities Press.Google Scholar
Bucenieks, I., Maniks, J., Simanovskis, A. & Muktepavela, F. 1997 Wetting of stainless steel by mercury. Trans. Am. Nucl. Soc. 77, 472.Google Scholar
Bühler, L., Horanyi, S. & Arbogast, E. 2007 Experimental investigation of liquid-metal flows through a sudden expansion at fusion-relevant Hartmann numbers. Fusion Engng Des. 82 (15–24), 22392245.CrossRefGoogle Scholar
Burattini, P., Zikanov, O. & Knaepen, B. 2010 Decay of magnetohydrodynamic turbulence at low magnetic Reynolds number. J. Fluid Mech. 657, 502538.Google Scholar
Cukierski, K. & Thomas, B.G. 2008 Flow control with local electromagnetic braking in continuous casting of steel slabs. Metall. Mater. Trans. B 39 (1), 94107.Google Scholar
Davidson, P.A. 1995 Magnetic damping of jets and vortices. J. Fluid Mech. 299, 153186.Google Scholar
Eckert, S., Gerbeth, G., Witke, W. & Langenbrunner, H. 2001 MHD turbulence measurements in a sodium channel flow exposed to a transverse magnetic field. Intl J. Heat Fluid Flow 22 (3), 358364.Google Scholar
Escudier, M.P., Oliveira, P.J. & Poole, R.J. 2002 Turbulent flow through a plane sudden expansion of modest aspect ratio. Phys. Fluids 14 (10), 36413654.Google Scholar
Hasimoto, H. 1960 Steady longitudinal motion of a cylinder in a conducting fluid. J. Fluid Mech. 8 (1), 6181.Google Scholar
Holroyd, R.J. 1979 An experimental study of the effects of wall conductivity, non-uniform magnetic fields and variable-area ducts on liquid metal flows at high Hartmann number. Part 1. Ducts with non-conducting walls. J. Fluid Mech. 93 (4), 609630.Google Scholar
Holroyd, R.J. & Walker, J.S. 1978 A theoretical study of the effects of wall conductivity, non-uniform magnetic fields and variable-area ducts on liquid-metal flows at high Hartmann number. J. Fluid Mech. 84 (3), 471495.Google Scholar
Hua, T.Q. & Walker, J.S. 1989 Three-dimensional MHD flow in insulating circular ducts in non-uniform transverse magnetic fields. Intl J. Engng Sci. 27 (9), 10791091.Google Scholar
Kalis, Kh.E. & Kolesnikov, Yu.B. 1984 Stability of a rotating transverse axisymmetric flow in an axial magnetic field. Magnetohydrodynamics 19 (3), 291294.Google Scholar
Kim, J. & Choi, H. 2004 Large eddy simulation of magnetic damping of jet. In International Congress of Theoretical and Applied Mechanics.Google Scholar
Kit, L.G., Peterson, D.E., Platnieks, I.A. & Tsinober, A.B. 1970 Investigation of the influence of fringe effects on a magnetohydrodynamic flow in a duct with nonconducting wall. Magnetohydrodynamics 6 (4), 485491.Google Scholar
Kljukin, A.A. & Kolesnikov, Yu.B. 1989 MHD instabilities and turbulence in liquid metal metal shear flows. In Liquid Metal Magnetohydrodynamics (ed. J. Lielpeteris & R. Moreau), pp. 449–454. Kluwer Academic.Google Scholar
Klyukin, A.A. & Thess, A. 1993 The investigation of the turbulence origination process in an electrically driven MHD flow. Magnetohydrodynamics 29 (4), 341344.Google Scholar
Kolesnikov, Yu.B. & Tsinober, A.B. 1972 Two-dimensional turbulent flow behind a circular cylinder. Magnetohydrodynamics 8 (3), 300307.Google Scholar
Krasnov, D., Akhtari, A., Zikanov, O. & Schumacher, J. 2022 Tensor-product-Thomas elliptic solver for liquid-metal magnetohydrodynamics. J. Comp. Phys. Pre-proof 111784.Google Scholar
Krasnov, D., Listratov, Ya., Kolesnikov, Yu., Belyaev, I., Pyatnitskaya, N., Sviridov, E. & Zikanov, O. 2021 Transformation of a submerged flat jet under strong transverse magnetic field. Europhys. Lett. 134 (2), 24003.CrossRefGoogle Scholar
Ludford, G.S.S. 1960 Inviscid flow past a body at low magnetic Reynolds number. Rev. Mod. Phys. 32 (4), 1000.CrossRefGoogle Scholar
Michalke, A. 1984 Survey on jet instability theory. Prog. Aerosp. Sci. 21, 159199.Google Scholar
Mistrangelo, C. 2006 Three-Dimensional MHD Flow in Sudden Expansions. Forschungszentrum Karlsruhe.Google Scholar
Mistrangelo, C. 2011 Topological analysis of separation phenomena in liquid metal flow in sudden expansions. Part 2. Magnetohydrodynamic flow. J. Fluid Mech. 674, 132162.CrossRefGoogle Scholar
Mistrangelo, C. & Bühler, L. 2007 Numerical investigation of liquid metal flows in rectangular sudden expansions. Fusion Engng Des. 82 (15–24), 21762182.CrossRefGoogle Scholar
Mistrangelo, C. & Bühler, L. 2010 Perturbing effects of electric potential probes on MHD duct flows. Exp. Fluids 48 (1), 157165.CrossRefGoogle Scholar
Moffatt, H.K. 1966 Electrically driven steady flows in magnetohydrodynamics. In Applied Mathematics, pp. 945–953. Springer.CrossRefGoogle Scholar
Moffatt, H.K. & Toomre, J. 1967 The annihilation of a two-dimensional jet by a transverse magnetic field. J. Fluid Mech. 30 (1), 6582.CrossRefGoogle Scholar
Molokov, S. 1993 Single-component magnetohydrodynamic flows in a strong uniform magnetic field. 2. Rotation of an axisymmetric body. Magnetohydrodynamics 29 (2), 175180.Google Scholar
Molokov, S. & Reed, C.B. 2003 Parametric study of the liquid metal flow in a straight insulated circular duct in a strong nonuniform magnetic field. Fusion Sci. Technol. 43 (2), 200216.CrossRefGoogle Scholar
Molokov, S.S., Moreau, R. & Moffatt, H.K. 2007 Magnetohydrodynamics: Historical Evolution and Trends, vol. 80. Springer.Google Scholar
Müller, U. & Bühler, L. 2001 Magnetofluiddynamics in Channels and Containers. Springer.CrossRefGoogle Scholar
Murgatroyd, W. 1953 CXLII. Experiments on magneto-hydrodynamic channel flow. Lond. Edinb. Dublin Philos. Mag. J. Sci. 44 (359), 13481354.CrossRefGoogle Scholar
Pothérat, A. & Klein, R. 2014 Why, how and when MHD turbulence at low becomes three-dimensional. J. Fluid Mech. 761, 168205.Google Scholar
Pothérat, A. & Klein, R. 2017 Do magnetic fields enhance turbulence at low magnetic Reynolds number? Phys. Rev. Fluids 2 (6), 063702.CrossRefGoogle Scholar
Sato, H. 1960 The stability and transition of a two-dimensional jet. J. Fluid Mech. 7 (1), 5380.Google Scholar
Sato, H. & Sakao, F. 1964 An experimental investigation of the instability of a two-dimensional jet at low Reynolds numbers. J. Fluid Mech. 20 (2), 337352.CrossRefGoogle Scholar
Schumacher, J., Krasnov, D. & Pandey, A. 2022 Thermal and magnetoconvection: Small Prandtl numbers and strong magnetic fields. In High Performance Computing in Science and Engineering, pp. 110–111. Garshing.Google Scholar
Smith, S.W. 1997 The Scientist and Engineer's Guide to Digital Signal Processing. California Technical Publishing. dspguide.comGoogle Scholar
Stanley, S.A., Sarkar, S. & Mellado, J.P. 2002 A study of the flow-field evolution and mixing in a planar turbulent jet using direct numerical simulation. J. Fluid Mech. 450, 377407.Google Scholar
Sukoriansky, S., Zilberman, I. & Branover, H. 1986 Experimental studies of turbulence in mercury flows with transverse magnetic fields. Exp. Fluids 4 (1), 1116.CrossRefGoogle Scholar
Thomas, F.O. & Goldschmidt, V.W. 1986 Structural characteristics of a developing turbulent planar jet. J. Fluid Mech. 163, 227256.Google Scholar
Timmel, K., Miao, X., Wondrak, T., Stefani, F., Lucas, D., Eckert, S. & Gerbeth, G. 2013 Experimental and numerical modelling of the fluid flow in the continuous casting of steel. Eur. Phys. J. 220 (1), 151166.Google Scholar
Verma, M.K. 2017 Anisotropy in quasi-static magnetohydrodynamic turbulence. Rep. Prog. Phys. 80 (8), 087001.CrossRefGoogle ScholarPubMed
Vogt, T., Ishimi, W., Yanagisawa, T., Tasaka, Y., Sakuraba, A. & Eckert, S. 2018 Transition between quasi-two-dimensional and three-dimensional Rayleigh–Bénard convection in a horizontal magnetic field. Phys. Rev. Fluids 3 (1), 013503.CrossRefGoogle Scholar
Zikanov, O., Belyaev, I., Listratov, Y., Frick, P., Razuvanov, N. & Sviridov, V. 2021 Mixed convection in pipe and duct flows with strong magnetic fields. Appl. Mech. Rev. 73 (1), 010801.CrossRefGoogle Scholar
Zikanov, O., Krasnov, D., Boeck, T. & Sukoriansky, S. 2019 Decay of turbulence in a liquid metal duct flow with transverse magnetic field. J. Fluid Mech. 867, 661690.CrossRefGoogle Scholar
Zikanov, O., Krasnov, D., Boeck, T., Thess, A. & Rossi, M. 2014 Laminar–turbulent transition in magnetohydrodynamic duct, pipe, and channel flows. Appl. Mech. Rev. 66 (3), 030802.CrossRefGoogle Scholar